Can MOND be ruled out at laboratory scale?

The empirical MOND explanation of galactic rotation curves involves switching over in the low acceleration regime from the Newtonian acceleration Gm/r^2 to the MOND acceleration term sqrt(Gm a_0)/r.

This is normally achieved using an "interpolation function" which effectively switches off one term and switches on the other when the Newtonian acceleration decreases past the MOND acceleration parameter a_0.

MOND is of course normally applied only on the scale of galaxies. However, if we consider a Cavendish-style laboratory experiment involving a mass of 1kg at a distance of 1m, the resulting acceleration Gm/r^2 = 6.67e-11 ms^-2 is less than the MOND acceleration parameter a_0 = 1.2e-10 ms^-2, so the MOND effect should be significant.

As the mass is increased and the distance is decreased, making the acceleration more easily measurable, the acceleration moves from the MOND regime into the Newtonian regime, but one would still expect a partial MOND acceleration effect if MOND were really related to acceleration thresholds. Such an acceleration would be proportional to sqrt(m)/r instead of the usual m/r^2.

Have such effects been ruled out by laboratory experiments? If so, this would prove that MOND could not work without taking into account additional physical effects in addition to the gravitational acceleration; for example, it might depend only on the total gravitational acceleration relative to some background space.

Another oddity with the MOND idea is that particles of a star experience accelerations orders of magnitude higher than the overall acceleration of the star, which might appear to mean that they should not exhibit the MOND acceleration. I think that if the MOND extrapolation function is chosen to simply give a linear sum of the MOND and Newtonian accelerations, this theoretical problem does not arise, although this would then also rule out the "total gravitational acceleration" explanation for why MOND does not affect laboratory experiments. If my maths is correct, the extrapolation function which achieves this effect is as follows:

if you haven't already seen it you might be interested in last year's paper by Bekenstein and Magueijo about the possibility of testing MOND (probably they meant the Bekenstein relativistic version, primarily) in the context of the solar system

there is only one paper in arxiv that has both those two author names, so it is easy to find by the arxiv search

if you haven't already seen it you might be interested in last year's paper by Bekenstein and Magueijo about the possibility of testing MOND (probably they meant the Bekenstein relativistic version, primarily) in the context of the solar system

there is only one paper in arxiv that has both those two author names, so it is easy to find by the arxiv search

Thanks very much for the reference. That paper makes it clear that the authors are assuming that MOND takes effect only when the gradient of the total Newtonian potential is less than the critical acceleration. This has the interesting side-effect of potentially creating "islands" of MOND-like behaviour where potential gradients cancel within the solar system, or between the solar system and the galactic background, giving an "absolute" acceleration relative to some background space of less than the critical value. That seems a nice theoretical idea, but I don't find it very plausible as physics.

If MOND only applies for small absolute accelerations, that would of course make it difficult to observe (or equally refute) MOND effects in a laboratory, but as I previously mentioned it also seems to raise questions about why a star as a whole should be affected by it at all, given that all of its component particles are experiencing local gravitational effects far exceeding the MOND threshold.

I'm currently interested in whether it's possible to use laboratory results to rule out the alternative of a simpler MOND-like acceleration effect which simply effectively adds sqrt(Gma_0)/r to everywhere to the Newtonian acceleration Gm/r^2. I suspect this may well be already known to be the case, and this would explain why these authors are assuming that MOND only relates to the total gradient. However, so far when I've searched for information about experiments to look for inverse square law deviations in the laboratory environment, they seem to be looking for accelerations which vary with 1/r^n where n > 2, but I'm interested in n < 2.

Of course, if laboratory experiments have not yet been sufficiently accurate to rule out local MOND effects, then that might relate to the well-known difficulties in getting a consistent value of G in different laboratory experiments. However, my guess is that there's already some results out there that can rule out this explanation.

...That paper makes it clear that the authors are assuming that MOND takes effect only when the gradient of the total Newtonian potential is less than the critical acceleration. ...

I think you have got it right. And I would consider Bekenstein (one of the two authors) to be the chief authority on MOND at the present time.
His "relativistic MOND" (also called TeVeS) has taken over a lot of the attention that used to be around Moti Milgrom 1980s nonrelativistic version.

So basically my attitude is whatever Jacob Bekenstein says MOND is, that is what it is, and if he says it depends on the total potential, then it does.

the alternative (that it depends on the effect of a single particle in the sun and that you add up all these effects) does not make sense to me. as I see it, there is one graviational field (which Bekenstein says consists of tensor, vector, and scalar parts) that exhibits MOND effects.

it does not make sense to me to consider that a single proton in the sun could make a field that would exhibit MOND effects in how it influences the earth. in that case essentially all the gravity we experience would be exhibiting obvious mond effects----which it doesnt

It does not make sense to me to consider that a single proton in the sun could make a field that would exhibit MOND effects in how it influences the earth. in that case essentially all the gravity we experience would be exhibiting obvious mond effects----which it doesnt

I'm not suggesting there's a problem with the way particles create the MOND field.

My point (which I believe is a well known one) is that if it's the total potential which creates the field, it is not clear why stars should be affected by the MOND acceleration at all, as a star is not a point particle but rather a collection of particles which are all falling within the star's own gravitational field and being pushed back up by thermal energy.

Even if MOND effects do apply locally, they are not very large, and although I believe they should be detectable, I'm not sure, hence this thread.

MOND does not appear to 'work' within out solar system. That imparts it disturbingly non-local consequences. Detecting gravitational effects in the laboratory at small scales is a different matter. It is not clear gravity even exists at short distances. It is overwhelmed by quantum effects.

"MOdified Newtonian Dynamics (MOND) is an interesting alternative to dark matter in extragalactic systems. We here examine the possibility that mild or even strong MOND behavior may become evident well inside the solar system, in particular near saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizeable oblate ellipsoid around the saddle point. We work out the MOND effects using the nonrelativistic limit of the TeVeS theory, both in the perturbative nearly Newtonian regime and in the deep MOND regime. While strong MOND behavior would be a spectacular 'backyard' vindication of the theory, pinpointing the MOND-bubbles in the setting of the realistic solar system may be difficult. Space missions, such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region."

MOND theory is so intersesting as well. First of all, the important point is the total garavitational acceleration, what i mean is that, we can not test MOND theor on Earth, the gravitational acceleration between Pluto and Mercury is higher than a0.Secondly, we dont see any dark matter affect if the total gravitational acceleration is less than a0 for any particular astronomical systems (this one is so interesting). Finally, there is sth with a0, that is a0=cH/6 (c:spped of light, Hubble constant).From this, we know that H is not actually a constant, it chances over time, that means the vaue of a0 should change over time, a0 should have higer value in the early universe-at least during infilation. Finally, I wanna say that MONd theory is a ad hoc way, yet this theory predicted excistance of LSB-low surface brightness galaxies.